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Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
1992 India National Olympiad
2
Inequality
Inequality
Source: INMO 1992 Problem 2
October 3, 2005
inequalities
Problem Statement
If
x
,
y
,
z
∈
R
x , y, z \in \mathbb{R}
x
,
y
,
z
∈
R
such that
x
+
y
+
z
=
4
x+y +z =4
x
+
y
+
z
=
4
and
x
2
+
y
2
+
z
2
=
6
x^2 + y^2 +z^2 = 6
x
2
+
y
2
+
z
2
=
6
, then show that each of
x
,
y
,
z
x, y, z
x
,
y
,
z
lies in the closed interval
[
2
3
,
2
]
\left[ \dfrac{2}{3} , 2 \right]
[
3
2
,
2
]
. Can
x
x
x
attain the extreme value
2
3
\dfrac{2}{3}
3
2
or
2
2
2
?
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